Equivariant deformation of minimally elliptic singularities

We study certain equivariant deformation components of minimally elliptic surface singularities under finite group actions. Interesting examples include cyclic quotients of simple elliptic singularities and finite group quotients of cusp singularities, where the resulting quotients remain simple elliptic and cusp singularities, respectively. In cases where the minimally elliptic singularities are locally complete intersection (lci) singularities, we identify equivariant deformation components of general type surfaces containing such singularities that admit a perfect obstruction theory.